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For $1\leq p\leq \infty$ and $\alpha>0$, Besov spaces $B^p_\alpha$ play a keyrole in the theory of $\alpha$-M\"obius invariant function spaces. In somesense, $B^1_\alpha$ is the minimal $\alpha$-M\"obius invariant function space,$B^2_\alpha$ is the unique $\alpha$-M\"obius invariant Hilbert space, and$B^\infty_\alpha$ is the maximal $\alpha$-M\"obius invariant function space. Inthis paper, under the $\alpha$-M\"obius invariant pairing and by the space$B^\infty_\alpha$, we identify the predual and dual spaces of $B^1_\alpha$. Inparticular, the corresponding identifications are isometric isomorphisms. Theduality theorem via the $\alpha$-M\"obius invariant pairing for $B^p_\alpha$with $p>1$ is also given.

Duality for $\alpha$-M\"obius invariant Besov spaces